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A bird starts from (1,0,0) in the direct...

A bird starts from `(1,0,0)` in the direction `(2hati+3hatj-6hatk)` with a speed `21 m//s` for `5` sec,then along the direction `(3hati+4hatj+5hatk)`with a speed `5sqrt2m//s` for `5` sec. Find the final displacement of the bird so that it reaches the origin?

A

`30hati+45hatj-45hatk`

B

`-45hati-65hatj+65hatk`

C

`-46hati-65hatj+65hatk`

D

`46hati-65hatj-65hatk`

Text Solution

Verified by Experts

The correct Answer is:
C
`vec(r_(i))=hat(j)`
`vec(d_(1))=21xx5[(2hat(i)+3hat(j)-6hat(k))/(7)]=30hat(i)+45hat(j)-90hat(k)`
`vec(d_(2))=5sqrt(2)xx5[[3hati+45hatj-90hatk]]/(5sqrt(2))`
`=15hat(i)+20hat(j)+25hat(k)`
`d_(Net)=45hati+65hatj-65hatk`
`rArrvec(r_(f))=46hat(i)+65hat(j)-65hat(k)`
For zero displacement
`vec(d_(f))=-(r_(f))=-(46hat(i)+65hat(j)-65hat(k))`
`=-46hat(i)-65hat(j)+65hat(k)`
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